How to Fix Flickering Lamp (That Stops Flickering When I Unscrew and Rescrew)

I just bought a set of two lamps (https://www.wayfair.com/lighting/pdp/alcott-hill-amell-2539-table-lamp-set-w003190357.html). The lamps have settings for off, low light, medium light, and high light which can be changed by just touching the base of the lamp.

I put 60 Hz LED bulbs in both lamps. One of the lamps starts to strobe more and more the brighter I turn up the light on it, as if the Hz drops as I turn up the brightness. I use the term strobing because the flashing occurs at a steady pace, not like erratic flickering.

The other lamp works fine with the same light bulb. I’ve tried multiple new bulbs and this happens every time. The weird thing is the LED bulb stays steady when I leave the lamp on, unscrew the bulb, and screw it back in. Now I have a morning routine of turning on the lamp, unscrewing and re-screwing the bulb and it works correctly all day until I turn it off and back on.

I don’t want to have to do this every time I turn the light on, so I was hoping someone on here might have experienced the same thing and can point me in the right direction for how to fix it.

The lamps now seem to be sold out so I don’t think I’ll end up getting a replacement but I’m trying that avenue as well.